Related papers: Nonholonomic Motion Planning as Efficient as Piano…
A visualized graph is a powerful tool for data analysis and synthesis tasks. In this case, the task of visualization constitutes not only in displaying vertices and edges according to the graph representation, but also in ensuring that the…
Graph drawing addresses the problem of finding a layout of a graph that satisfies given aesthetic and understandability objectives. The most important objective in graph drawing is minimization of the number of crossings in the drawing, as…
This paper introduces a hierarchical framework that integrates graph search algorithms and model predictive control to facilitate efficient parking maneuvers for Autonomous Vehicles (AVs) in constrained environments. In the high-level…
Lifelong SLAM considers long-term operation of a robot where already mapped locations are revisited many times in changing environments. As a result, traditional graph-based SLAM approaches eventually become extremely slow due to the…
Triangle counting is a fundamental building block in graph algorithms. In this paper, we propose a block-based triangle counting algorithm to reduce data movement during both sequential and parallel execution. Our block-based formulation…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
Path cover is a well-known intractable problem that finds a minimum number of vertex disjoint paths in a given graph to cover all the vertices. We show that a variant, where the objective function is not the number of paths but the number…
Graph coarsening is a graph dimensionality reduction technique that aims to construct a smaller and more tractable graph while preserving the essential structural and semantic properties of the original graph. However, most existing methods…
This paper develops different discretization schemes for nonholonomic mechanical systems through a discrete geometric approach. The proposed methods are designed to account for the special geometric structure of the nonholonomic motion. Two…
In this paper, we address the numerical solution of the Optimal Transport Problem on undirected weighted graphs, taking the shortest path distance as transport cost. The optimal solution is obtained from the long-time limit of the gradient…
We present an algorithm for planning trajectories that avoid obstacles and satisfy key-door precedence specifications expressed with a fragment of signal temporal logic. Our method includes a novel exact convex partitioning of the obstacle…
This paper presents a hybrid motion planning strategy that combines a deep generative network with a conventional motion planning method. Existing planning methods such as A* and Hybrid A* are widely used in path planning tasks because of…
This paper focuses on the motion planning for mobile robots in 3D, which are modelled by 6-DOF rigid body systems with nonholonomic kinematics constraints. We not only specify the target position, but also bring in the requirement of the…
We train an agent to navigate in 3D environments using a hierarchical strategy including a high-level graph based planner and a local policy. Our main contribution is a data driven learning based approach for planning under uncertainty in…
Pose graph optimization (PGO) is fundamental to robot perception and navigation systems, serving as the mathematical backbone for solving simultaneous localization and mapping (SLAM). Existing solvers suffer from polynomial growth in…
We study the complexity of counting (weighted) planar graph homomorphism problem $\tt{Pl\text{-}GH}(M)$ parametrized by an arbitrary symmetric non-negative real valued matrix $M$. For matrices with pairwise distinct diagonal values, we…
A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more…
We prove a complexity dichotomy theorem for a class of Holant problems on planar 3-regular bipartite graphs. The complexity dichotomy states that for every weighted constraint function $f$ defining the problem (the weights can even be…
The advent of new special-purpose hardware such as FPGA or ASIC-based annealers and quantum processors has shown potential in solving certain families of complex combinatorial optimization problems more efficiently than conventional CPUs.…
We present a new parallel algorithm for $k$-clique counting/listing that has polylogarithmic span (parallel time) and is work-efficient (matches the work of the best sequential algorithm) for sparse graphs. Our algorithm is based on…